I'm trying to understand the increase of entropy just after the big bang. The way i see it going from a "soup" of particles to organized and ordered sytems like solar system, galaxies and clouster of galaxies would suggest decrease of entropy?
You are concentrating on the soup of particles and do not count the soup of radiation, the zero mass particles. Just acceleration and deceleration of of charged particles generates radiation. The accumulation into galaxies and star systems would release gravitational radiation. The stars themselves release black body radiation all the time from their creation on. Any matter releases black body radiation, so it is a no win situation for a decrease of entropy.